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A sector is a portion of a circle bounded by two radii and the arc joining their extremities. It is thus a form of triangle with a covered base. In the figure the portion  is a sector. Arc  is called the arc of the sector and  is called the angle of the sector.
The area of a sector of a circle is equal to a fraction of the area of the circle determined by dividing the size of the angle by . Thus, if the angle of the sector is  , the area of the sector is  or  the area of the circle, that is, i.e., the area of a sector bears that portion to the area of the circle which its angle bears to  right angles i.e.,  .
(a) If the angle  is given in degrees, say , then
Area of the sector, 
Length of the arc, 
(b) If the angle  is given in radians, say  radians, then
Area of the sector, 
(c) If the length  of the arc and the radius  of the circle are given, then
Area of the sector,  where 
Example:
Find the area of a sector of  in a circle of radius  cm.
Solution:
The sector  has angle .
Its area is equal to 
Since radius  cm
Therefore  Square
Example:
The minute hand of a clock is  cw long. Find the area which is described on the clock face between  A.M to  A.M.
Solution:
Given that, Length of minute hand, radius  cm
  Minutes 
  Minutes 
Since, Area of sector 
 Square cm
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